Ambrosetti-Prodi-type results for a third order multi-point boundary value problem. (English) Zbl 1205.34020
Summary: The authors study the third order boundary value problem
\[ u'''=f(t,u)+\lambda e(t),\quad t\in(0,1), \]
\[ u(0)=u'(p)=\int^1_q w(s)u''(s)\,ds = 0. \]
Using the lower and upper solution method and fixed point index theory, some Ambrosetti-Prodi-type results are obtained for the above problem.
\[ u'''=f(t,u)+\lambda e(t),\quad t\in(0,1), \]
\[ u(0)=u'(p)=\int^1_q w(s)u''(s)\,ds = 0. \]
Using the lower and upper solution method and fixed point index theory, some Ambrosetti-Prodi-type results are obtained for the above problem.
MSC:
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
